They did. Multiple branches, even, at least partly due to inter-service rivalries, with the Abwehr, the SD, the navy, the air force, and the SS developing their own branches (the army inheriting its special forces from the Abwehr). The main special forces branch was the Brandenburgers, originally formed by the Abwehr, and transferred to the army after the invasion of Poland. The Brandenburgers began the war as a batallion, and grew to being a division. They saw action in the invasions of Poland, Norway, the Low Countries, the Balkans, and also in North Africa and on the Eastern Front, and in anti-partisan operations in the Balkans.

SS special forces famously rescued Mussolini (together with Luftwaffe special forces, who provided the bulk of the manpower), and operated disguised as American forces during the Ardennes Offensive (Operation Greif); both of these were commanded by Otto Skorzeny.

The Kriegsmarine special forces, the Marinestosstruppkompanie, predated the start of the war, and had seen action during the Spanish Civil War.

The Luftwaffe had both air and ground special forces. The air branch was Kampfgeschwader 200, which carried out various special air operations, and Sonderkommando Elbe, tasked with ramming Allied heavy bombers, could also be considered "special forces". The ground branch was basically airborne forces (Fallschirmjäger) used in special forces roles (with notable success early in the war with the capture of the Belgian Fort Ebn-Emael).

For more, see James Lucas, Kommando: German Special Forces of World War Two, Arms and Armour Press, 1985 (reprinted by Frontline Books, 2014).